We repeated the demagnetization cycle for various final fields, shown in Fig. REF (a), to gain insight into the nature of the heat leaks. If a constant heat leak is present, the plot of the inverse temperature as a function of time turns out to be linear, and the slope can be used to extract the heat leak [1]}, [2]}. For both \(B_\mathrm {f}\) =120 mT and 150 mT, the curves are indeed linear for up to 40 or 50 hours, when finally a rapid warmup occurs. For the two lower final fields, however, the warmup curve is initially nonlinear, allowing a good linear fit only several hours after the end of the ramp down. In the nonlinear regime, the CBT consistently reads a higher temperature compared to the back-extrapolated linear fit (black dashed lines). This may be attributed to voltage noise \(V_\mathrm {n}\)  across the CBT leads. Due to the very narrow conductance dip at the lowest temperatures, voltage noise effectively averages over the center of the conductance dip, and artificially increases \(g_0\)  readings which in turn produce higher apparent CBT temperatures. This can be calculated by smearing the MCMC model of \(g(V_\mathrm {sd})\)  with gaussian noise. Choosing noise values around \(V_\mathrm {n}\) =1 µVrms, as labelled, makes the model (grey curves) almost entirely coincide with the measured temperatures. Given the good agreement, this makes the extrapolated temperature of 189 µK quite plausible as the actual electron temperature when the CBT reads 265 µK at the beginning of the warmup at \(B_\mathrm {f}\) =60 mT.
